As they tumble through space, objects like spacecraft move in dynamical ways. Understanding and predicting the equations that represent that motion is critical to the safety and efficacy of spacecraft mission development. Kinetics: Modeling the Motions of Spacecraft trains your skills in topics like rigid body angular momentum and kinetic energy expression shown in a coordinate frame agnostic manner, single and dual rigid body systems tumbling without the forces of external torque, how differential gravity across a rigid body is approximated to the first order to study disturbances in both the attitude and orbital motion, and how these systems change when general momentum exchange devices are introduced.
After this course, you will be able to...
*Derive from basic angular momentum formulation the rotational equations of motion and predict and determine torque-free motion equilibria and associated stabilities
* Develop equations of motion for a rigid body with multiple spinning components and derive and apply the gravity gradient torque
* Apply the static stability conditions of a dual-spinner configuration and predict changes as momentum exchange devices are introduced
* Derive equations of motion for systems in which various momentum exchange devices are present
Please note: this is an advanced course, best suited for working engineers or students with college-level knowledge in mathematics and physics.

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Gravity Gradients

The differential gravity across a rigid body is approximated to the first order to study how it disturbs both the attitude and orbital motion. The gravity gradient relative equilibria conditions are derived, whose stability is analyzed through linearization.

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Hanspeter Schaub

Glenn L. Murphy Chair of Engineering, Professor

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Hi and welcome to the third segment of Spacecraft Kinetics. Here, we're going to be studying in detail the gravity gradient, torque and forces that happen on a rigid spacecraft. So with the spacecraft, every part of the mass distribution is a different distance away from the center of the Earth. That means it's experiencing a different gravitational force. Now, we have to sum it up over a whole body. So in particular of interest to us is if you have the gravity gradient that you've computed, which orientations of a craft caused the gravity gradient to be zero. And when we're moving in a rotating frame, which one of these are now relative equilibrious will be developing all of those and then there's some interesting examples. You can look at which one of those is stable. Look at a tall slender object, the lower object weighs more has a stronger gravity force than the top part. So if you disturb the attitude, this would help stabilize it. We'll begin to study such configuration for full 3D. This is a very useful topic. There's many satellites of gravity being stabilized or there are big things like the space station. Gravity gradients definitely impact the attitude motion. So, this section gives you a good handle on how to predict that torque.